The lifespans of snakes in a particular zoo are normally distributed. The average snake lives $27$ years; the standard deviation is $2.6$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a snake living between $21.8$ and $32.2$ years.
Answer: $27$ $24.4$ $29.6$ $21.8$ $32.2$ $19.2$ $34.8$ $95\%$ We know the lifespans are normally distributed with an average lifespan of $27$ years. We know the standard deviation is $2.6$ years, so one standard deviation below the mean is $24.4$ years and one standard deviation above the mean is $29.6$ years. Two standard deviations below the mean is $21.8$ years and two standard deviations above the mean is $32.2$ years. Three standard deviations below the mean is $19.2$ years and three standard deviations above the mean is $34.8$ years. We are interested in the probability of a snake living between $21.8$ and $32.2$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $95\%$ of the snakes will have lifespans within 2 standard deviations of the average lifespan. The probability of a particular snake living between $21.8$ and $32.2$ years is ${95\%}$.